Problem: $f(x)=\dfrac{2}{1-3x^2}$ Find a power series for $f$. Choose 1 answer: Choose 1 answer: (Choice A) A $1+3x^2+9x^4+\ldots +3^n x ^{2n}+\ldots$ (Choice B) B $2+6x^2+18x^4+\ldots +2\cdot 3^n x ^{2n}+\ldots$ (Choice C) C $2-6x^2+18x^4+\ldots +(-2)^n\cdot 3^n x ^{2n}+\ldots$ (Choice D) D $2-6x^2-18x^4+\ldots -2\cdot 3^n x ^{2n}+\ldots$
Explanation: This is a geometric series with first term $a\text{ }=\text{ }2$ and common ratio $r\text{ }=\text{ }3x^2$. Therefore, the series is as follows. $2+6x^2+18x^4+\ldots +2\cdot 3^n x ^{2n}+\ldots $